Spaces and groups with conformal dimension greater than one

John M. Mackay

doi:10.1215/00127094-2010-023

Spaces and groups with conformal dimension greater than one

John M. Mackay^*

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

14 Citations (Scopus)

Abstract

We show that if a complete, doubling metric space is annularly linearly connected, then its conformal dimension is greater than one, quantitatively. As a consequence, we answer a question of Bonk and Kleiner: if the boundary of a one-ended hyperbolic group has no local cut points, then its conformal dimension is greater than one.

Original language	English
Pages (from-to)	211-227
Number of pages	17
Journal	Duke Mathematical Journal
Volume	153
Issue number	2
DOIs	https://doi.org/10.1215/00127094-2010-023
Publication status	Published - 1 Jun 2010

Keywords

HYPERBOLIC GROUPS
ARCS
BOUNDARY
METRIC-SPACES

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http://projecteuclid.org/euclid.dmj/1274902080

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title = "Spaces and groups with conformal dimension greater than one",

abstract = "We show that if a complete, doubling metric space is annularly linearly connected, then its conformal dimension is greater than one, quantitatively. As a consequence, we answer a question of Bonk and Kleiner: if the boundary of a one-ended hyperbolic group has no local cut points, then its conformal dimension is greater than one.",

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T1 - Spaces and groups with conformal dimension greater than one

AU - Mackay, John M.

PY - 2010/6/1

Y1 - 2010/6/1

N2 - We show that if a complete, doubling metric space is annularly linearly connected, then its conformal dimension is greater than one, quantitatively. As a consequence, we answer a question of Bonk and Kleiner: if the boundary of a one-ended hyperbolic group has no local cut points, then its conformal dimension is greater than one.

AB - We show that if a complete, doubling metric space is annularly linearly connected, then its conformal dimension is greater than one, quantitatively. As a consequence, we answer a question of Bonk and Kleiner: if the boundary of a one-ended hyperbolic group has no local cut points, then its conformal dimension is greater than one.

KW - HYPERBOLIC GROUPS

KW - ARCS

KW - BOUNDARY

KW - METRIC-SPACES

U2 - 10.1215/00127094-2010-023

DO - 10.1215/00127094-2010-023

M3 - Article (Academic Journal)

SN - 0012-7094

VL - 153

SP - 211

EP - 227

JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

IS - 2

ER -

Spaces and groups with conformal dimension greater than one

Abstract

Keywords

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